Quantum Error Correcting Code Empirical Performance

This site is under construction.
Please contact David MacKay with your codes' performance details.

The above figure shows performance results for the codes
published in our paper.
The captions of the relevant figures are given below.

Summary of performances of several quantum codes
on the 4-ary symmetric channel (depolarizing channel),
treated (by almost all the decoding algorithms shown in this figure)
as if the channel were a pair of independent binary symmetric
channels.
Each point shows the (horizontal axis) marginal
noise level at which the block error probability
is $10^{-4}$.
In the case of dual-containing codes,
this is the noise level at which each of the two identical
constituent codes has an error probability of $5\times 10^{-5}$.
As an aid to the eye, lines have been added between the four unicycle codes (U);
between a sequence of bicycle codes (B) all of blocklength $N=3786$
with different rates;
and between a sequence of of BCH codes with increasing blocklength.
The curve labelled S2 is the Shannon limit if the correlations
between X errors and Z errors are neglected.
Points `$+$' are codes invented elsewhere. All other point styles
denote codes presented for the first time in this paper.
Summary of performances of several codes
on the 4-ary symmetric channel (depolarizing channel).
The additional points at the right and bottom are as follows.
3786(B,4SC): a code of construction B (the same code as its
neighbour in the figure) decoded with a decoder
that exploits the known correlations between X errors and Z errors.
3786(B,D): the same code as the $N=3786$ code to its
left in the figure, simulated with a channel where
the qubits have a diversity
of known reliabilities; X errors and Z errors occur independently
with probabilities determined from a Gaussian distribution; the channel
in this case is not the 4-ary symmetric channel, but we
plot the performance at the equivalent value of the marginal noise level.
[[29,1,11]]: an algebraically constructed quantum code (not a sparse-graph code)
from Markus Grassl.